In the build up to this work, we in fact realized Equations (REF ) and (REF ) first as derivation operators before observing that they are homotopy lifting maps. It was remarked in [1]}, that for an \(n\) -cocycle \(g\) , there is an associated homotopy lifting map \(\psi _g\)  which can also be realized as a coderivation on the tensor algebra of \(A\) . If \(g\)  is a 1-cocycle, then \(\psi _g\)  may be extended to a derivation operator \(\tilde{g}\)  in some sense. This describes how a derivation operator may be obtained from a homotopy lifting map. Question REF  asks whether the converse of this observation is true.
